Please try:
ALTER DATABASE "popbio-v4.1.1-VB-2014-04-prod-03" RENAME TO "popbio-v4.1.1-VB-2014-04-prod-04";
this should work. At least it did locally:
postgres=# create database "popbio-v4.1.1-VB-2014-04-prod-03";
CREATE DATABASE
postgres-# \l
...
popbio-v4.1.1-VB-2014-04-prod-03 | postgres | UTF8 | de_DE.UTF-8 | de_DE.UTF-8 |
...
postgres=# ALTER DATABASE "popbio-v4.1.1-VB-2014-04-prod-03" RENAME TO "popbio-v4.1.1-VB-2014-04-prod-04";
ALTER DATABASE
postgres=# \l
...
popbio-v4.1.1-VB-2014-04-prod-04 | postgres | UTF8 | de_DE.UTF-8 | de_DE.UTF-8 |
...
Also on PostgreSQL you don't have user databases. Users can only have rights on special databases or can own them. Of course you cannot do this as a normal user without any gratings.